Simultaneous call transmission detection

ABSTRACT

A method of determining the presence of a secondary carrier signal in a time-domain sum-signal including a primary carrier signal is disclosed, the method comprising: transforming the sum-signal into the frequency domain; extracting at least one peak corresponding to a heterodyne tone from the transformed sum-signal; determining the presence of a secondary carrier signal in the sum-signal based on said at least one peak. A corresponding apparatus is also disclosed.

FIELD OF INVENTION

This invention relates to an apparatus and method for the detection ofsimultaneous call transmissions, in particular to double-sidebandamplitude modulation (DSB-AM) transmissions.

BACKGROUND

Simultaneous Call Transmissiofn (SCT) is a situation when two or moretransmissions occur simultaneously on the same frequency band. The endlistener is then (usually) only able to understand the higher powered ofthe pair of transmissions. An example is illustrated in FIG. 1.

This is a potentially hazardous situation as the sender of the weakertransmission may assume that they were actually heard by the endlistener and take action accordingly. A situation where the consequentaction would be incredibly dangerous would be where two planes transmita signal to an air-traffic controller simultaneously, who then replies,and both planes believe the response is directed to them. Such ascenario may be noticed by an alert, trained human operator listeningout for the characteristic phenomena of interfering voice and heterodynetones arising from the frequency difference between the twotransmitters. However this only reliably works when the weakertransmitter is (1) within the power range of the stronger transmittere.g. 0 to −20 dB and (2) the heterodyne lies in the filtered audio range(e.g. 300 Hz to 3.5 kHz). The first condition may not be met if onetransmission originates much further away than the other (i.e. one planeis overhead and the other is several kilometres away); the secondcondition may not be met if the frequency difference between the twotransmitters (defined by the precision of the quartz in the transmittingequipment) is minor.

Indeed, SCT can occur far outside of these values due to real worldeffects such as propagation loss, multipath error and frequency error.

Hence automatic SCT detection is a desirable feature for radios.

US2010/0067570A1 describes an apparatus adapted to automatically detectwhen two transmissions occur simultaneously. This system phasedemodulates the sum-signal of the dual transmission by converting thebaseband In-Phase and Quadrature signal into unwrapped phase andamplitude. A periodic ‘wobble’ is present on the unwrapped phase ifthere are close frequency-separated transmissions, as the difference infrequency causes the phasors of the transmissions to rotate around oneanother. This phase time-series is then Fourier transformed using a bankof transformers with varying window lengths to determine whether anysecondary transmission (i.e. a peak due to the unwrapped phase ‘wobble’)is present. A warning tone is added to the audio output if a secondarytransmission is detected so as to alert the operator to the situation.

This proposed solution has several significant drawbacks. The step ofproducing a phase time series is an intrinsically non-linear process (asit involves performing an arctan) and so errors propagate as the processprogresses manifesting as intermodulation products in the outputspectrum which are not physically present in the input. Furthermore, inreal-world conditions this solution can potentially generate largeoccurrences of ‘false positives’ where an alert is sounded when only onetransmission is present. This is because this system has no way ofsuppressing common signal impairments such as sinusoidal mains hum,incidental FM (frequency modulation), frequency-selective multipatheffects and 1/f² (reciprocal frequency-squared) phase noise. All ofthese effects can potentially introduce a certain amount of unwrappedphase ‘wobble’ and then be identified as secondary transmissions.

False positives are very damaging because they cause an operator to losefaith in the equipment's reliability if it is ‘crying wolf’ too often.This may result in the operator turning off the automatic SCT featurecompletely or taking unnecessary mitigating action such as repetition ofinstructions. Because Air Traffic Control is a safety critical activity,an SCT detection system should be highly tolerant to real signalimperfections so that it is of the highest achievable reliability.

On the other hand, false negatives are inevitable when the secondarytransmission is very weak in power, when it becomes indiscernible fromthe noise floor, and also in the situation where the secondarytransmission is superposed on the stronger transmission with negligiblefrequency difference.

An improved solution is therefore needed.

In one embodiment there is provided a method of determining the presenceof a secondary carrier signal in a time-domain sum-signal including aprimary carrier signal, the method comprising: transforming thesum-signal into the frequency domain; extracting at least one peakcorresponding to a heterodyne tone from the transformed sum-signal;determining the presence of a secondary carrier signal in the sum-signalbased on said at least one peak. Such a method provides an efficient wayof determining the presence of a secondary carrier signal in atime-domain sum-signal in a manner resistant to false positives;specifically in a linear manner which does not introduce intermodulationproducts.

Preferably, the method further comprises identifying a primary carriersignal within the sum-signal.

Preferably, the method further comprises determining a conjugate of asideband of the frequency-domain primary carrier signal and attenuatingthe primary carrier by using said conjugate of the sideband of theprimary signal

Preferably, the conjugate of the sideband of the primary signal issubtracted from the opposing frequency sideband of the sum-signal.

Preferably, the step of transformation into the frequency domain isperformed using a Fourier Transform (FT).

Preferably, the step of transformation into the frequency domain isperformed using a discrete transform comprising input and output bins.

Preferably, the signal is split and mapped onto the input of a transformwith a larger size than the signal, wherein a central part of thetransform comprises zero-valued input bins are placed.

Preferably, a second half of the signal is mapped onto a first part ofthe transform input and a first half of the signal is mapped onto afinal part of the transform input.

Preferably, identifying a primary carrier signal comprises estimating aprimary carrier frequency.

Preferably, estimating the frequency of a primary carrier comprisesdetermining at least one highest magnitude frequency output bin anddetermining the peak frequency. This is a computationally efficient wayof determining the peak frequency.

Preferably, the three highest frequency output bins are determined and aquadratic curve is fitted so as to interpolate the peak frequency. Thisachieves a more accurate estimation of peak frequency compared to thefrequency bin with highest magnitude.

Preferably, the method further comprises down-converting thefrequency-domain sum signal based on said estimated frequency.

Preferably, the method further comprises phase-rotating thefrequency-domain down-converted sum-signal;

Preferably, the down-conversion is performed by convolving the FT outputwith a window filter. Preferably, the window filter comprises aclosed-form cosine function.

Preferably, the window filter comprises a Blackman family window,preferably Blackman-Nuttall window.

Preferably, the window filter comprises one of Kaiser or Equiripple.

Preferably, determining the presence of a secondary transmissioncomprises performing a symmetry analysis on said peak.

In another embodiment there is provided a method of determining thepresence of a second carrier signal in a time-domain sum-signal, themethod comprising: identifying a primary carrier signal within thesum-signal; attenuating the primary carrier signal from within the sumsignal; extracting at least one peak corresponding to a heterodyne tone;performing a symmetry analysis on said at least one peak to determinethe presence of a secondary transmission. Such a method provides anefficient way of determining the presence of a secondary carrier signalin a time-domain sum-signal in a manner resistant to false positives;specifically, the symmetry analysis reduces the chance of symmetricnoise effects being considered as a secondary carrier signal.

Preferably, identifying a primary carrier signal comprises estimating aprimary carrier frequency.

Preferably, identifying a primary carrier signal comprises estimatingthe phase of the primary carrier.

Preferably, the method comprises transforming the sum-signal into thefrequency domain.

Preferably, estimating the frequency of a primary carrier within thesum-signal comprises determining at least one highest magnitudefrequency output bin and determining the peak frequency.

Preferably, the phase estimation is performed by determining at leastone highest magnitude frequency output bin and determining the phase ofthe peak frequency component.

Preferably, the three highest frequency output bins are determined and acurve is fitted so as to interpolate the peak frequency.

Preferably, the fitted curve is a quadratic curve.

Preferably, following down-conversion, the quadrature component of thetime-domain sampled signal is transformed into the frequency domainprior to peak extraction.

Preferably, the down-converting comprises mixing the sampled signal witha sinusoid with a frequency and phase corresponding to an estimatedfrequency and phase of the primary carrier.

Preferably, the transformation into the frequency domain is a FourierTransform (FT), preferably a Fast Fourier Transform (FFT).

Preferably, the symmetry analysis comprises: determining a measure ofthe ratio of the magnitude of a peak at a certain frequency above acentral frequency with the magnitude of the signal at the correspondingfrequency below the central frequency. This ratio is an easilycalculated measure of the symmetry of a particular feature.

Preferably, the method comprises comparing said asymmetry ratio to apre-determined threshold.

Preferably, the magnitude of the peak is used in conjunction with saidratio in determining the presence of a secondary transmission.

Preferably, the method comprises producing a confidence score of asecondary carrier transmission being present based on the peak magnitudeand asymmetry ratio.

Preferably, the presence of a secondary transmission is determined onlyif a peak corresponding to the carrier of a primary transmission ispresent.

Preferably, the presence of a secondary transmission is determined onlyif the magnitude of said primary carrier peak is above a pre-determinedthreshold.

Preferably, the presence of a secondary transmission is determined onlyif the width of said primary carrier peak is below a pre-determinedfrequency threshold.

Preferably, following peak extraction, if two peaks are within a minimumfrequency separation of one another, the peaks are combined into asingle peak prior to determination of the presence of a secondarycarrier.

Preferably, the minimum frequency separation is between 5 Hz and 50 Hz,preferably between 7 Hz and 15 Hz, preferably approximately 10 Hz.

Preferably, the peak with the lower magnitude is discarded.

Preferably, the sum-signal is decimated so as to reduce the bandwidth.

Preferably, the frequency domain transform output is gain-transformed soas to compensate for decimator ripple.

Preferably, the gain transformation is the reciprocal of the gain due tothe magnitude spectrum response of the decimator.

Preferably, the sum-signal is sampled.

Preferably, the sum-signal is sampled in overlapping blocks.

Preferably, the sampling consists of the most recent T seconds of thesignal and the sampling rate is M times per second, where T*M>1.

Preferably, T is between 1 and 4, and M is between 2 and 8.

Preferably, T=2 and M=4.

Preferably, the method further comprises: estimating a noise floor ofthe down-converted signal; subtracting a measure said noise floor fromthe signal prior to peak extraction.

Preferably, wherein the noise floor estimation comprises performing amoving-average.

Preferably, the moving average comprises summing contiguous blocks of D₁samples and calculating the median across D₂ of said blocks.

Preferably, D₁ is approximately equal to D_(2.)

Preferably, the method further comprises alerting an operator to thepresence of a secondary transmission.

Preferably, alerting an operator comprises inserting a tone into anaudio output or a flag into a datastream.

Preferably, alerting an operator comprises indicating the presence of asecondary transmission on a user interface.

Preferably, alerting an operator comprises indicating the confidencelevel of the presence of a secondary transmission.

In another embodiment there is provided a method of reducing windowingartefacts in a time/frequency transform of a signal,: applying saidwindowing function to a signal; mapping the signal onto the input of anoversampled transform; wherein a central part of the transform input haszero-valued input bins; performing a time/frequency transform;outputting a frequency spectrum of the signal. Such a method reducesartefacts being brought into the signal which may be incorrectlyidentified as a secondary carrier signal.

Preferably the transform is a Fourier transform

Preferably, a second half of the signal is mapped onto a first part ofthe transform input and a first half of the signal is mapped onto afinal part of the transform input.

Preferably, the method further comprises the step of determining thepresence of a secondary carrier signal from the frequency spectrum ofthe signal.

Preferably, the method further comprises alerting a user to the presenceof a secondary carrier signal.

Preferably, the signal comprises voice communication.

Preferably, the voice communication is transmitted from an aircraft andintended to be received by an air traffic controller.

In another embodiment there is provided an apparatus adapted to carryout a method according to any preceding claim.

In another embodiment there is provided an apparatus for determining thepresence of a secondary carrier signal in a time-domain sum-signalincluding a primary carrier signal, the apparatus comprising: means fortransforming the sum-signal into the frequency domain; means forextracting at least one peak corresponding to a heterodyne tone from thetransformed sum-signal; means for determining the presence of asecondary carrier signal in the sum-signal based on said at least onepeak.

In another embodiment there is provided an apparatus for determining thepresence of a second carrier signal in a time-domain sum-signal, themethod comprising: means for identifying a primary carrier signal withinthe sum-signal; means for attenuating the primary carrier signal fromwithin the sum signal; means for extracting at least one peakcorresponding to a heterodyne tone; means for performing a symmetryanalysis on said at least one peak to determine the presence of asecondary transmission.

In another embodiment there is provided an apparatus for reducingwindowing artefacts in a time/frequency transform of a signal: means forapplying a windowing function to a signal; means for mapping the signalonto the input of an oversampled transform; wherein a central part ofthe transform input has zero-valued input bins; means for performing atime/frequency transform; means for outputting a frequency spectrum ofthe signal.

Preferably, the apparatus comprising a radio.

The invention extends to any novel aspects or features described and/orillustrated herein. Further features of the invention are characterisedby the other independent and dependent claims

Any feature in one aspect of the invention may be applied to otheraspects of the invention, in any appropriate combination. In particular,method aspects may be applied to apparatus aspects, and vice versa.

Furthermore, features implemented in hardware may be implemented insoftware, and vice versa. Any reference to software and hardwarefeatures herein should be construed accordingly.

The invention also provides a computer program and a computer programproduct comprising software code adapted, when executed on a dataprocessing apparatus, to perform any of the methods described herein,including any or all of their component steps.

The invention also provides a computer program and a computer programproduct comprising software code which, when executed on a dataprocessing apparatus, comprises any of the apparatus features describedherein.

The invention also provides a computer program and a computer programproduct having an operating system which supports a computer program forcarrying out any of the methods described herein and/or for embodyingany of the apparatus features described herein.

The invention also provides a computer readable medium having storedthereon the computer program as aforesaid.

The invention also provides a signal carrying the computer program asaforesaid, and a method of transmitting such a signal.

Any apparatus feature as described herein may also be provided as amethod feature, and vice versa. As used herein, means plus functionfeatures may be expressed alternatively in terms of their correspondingstructure, such as a suitably programmed processor and associatedmemory.

It should also be appreciated that particular combinations of thevarious features described and defined in any aspects of the inventioncan be implemented and/or supplied and/or used independently.

In this specification the word ‘or’ can be interpreted in the exclusiveor inclusive sense unless stated otherwise.

The invention extends to methods and/or apparatus substantially asherein described with reference to the accompanying drawings.

Purely by way of example, the present invention is illustrated by theaccompanying drawings in which:

FIG. 1 shows a Simultaneous Call Transmission (SCT) scenario;

FIG. 2 shows an example Double Side-Band Amplitude Modulated (DSB AM)signal;

FIG. 3 is an example flow diagram of an SCT detection method;

FIG. 4 is a schematic diagram of an apparatus operable to perform themethod shown in FIG. 3;

FIG. 5 shows overlapping windows of the sliding window buffer of FIG. 3;

FIG. 6 is an illustration of the ‘zero padded FFT’ of FIG. 3;

FIG. 7 shows example filters for use in an SCT detection method;

FIG. 8 shows the effect of the filters of FIG. 7 on an exampletime-domain equivalent (FFT input) envelope;

FIG. 9(a) shows an example frequency plot of a secondary signal,superposed on a primary signal carrying voice and 400 Hz mainsinterference present;

FIG. 9(b) shows the signal of FIG. 9(a) following down-conversion;

FIG. 10(a) shows the left hand side of the signal of FIG. 9(b) reflectedonto the right hand side;

FIG. 10(b) shows the signal of FIG. 10(a) following DSB-AM cancellationand a noise floor estimate;

FIG. 11(a) shows the signal of FIG. 10(b) following noise floorestimation;

FIG. 11(b) shows the asymmetry metric of the peaks detected from thesignal of FIG. 10(a);

FIG. 12 shows a ‘feature space’ plot of the peak and asymmetry metricsof a large number of simulations;

FIG. 13(a) shows a scenario where an SCT and 400 Hz mains noise areabsent;

FIG. 13(b) shows a scenario where an SCT is present and 400 Hz mainsnoise is absent;

FIG. 13(c) shows a scenario where an SCT and 400 Hz mains noise arepresent;

FIG. 14 shows a flow diagram of an alternative method for SCT detection;and

FIG. 15 is an illustration of the in-phase and quadrature components ofa signal where an SCT is present.

DETAILED DESCRIPTION

In this specification, the term ‘primary transmission’ or ‘primarycarrier’ refers to the transmission with greatest power. The term‘secondary transmission’ or ‘secondary carrier’ refers to any other(lower-powered) transmission occurring at the same time from anotheraircraft.

Air traffic controller (ATC) to aircraft communication is generally veryconcise, each transmission is typically less than 10 seconds induration, and can be as short as 2 or 3 seconds. For this reason, thelatency in detecting a secondary call transmission (SCT) is preferablyless than 2-3 seconds for this field of use. The term ‘simultaneous’ inthis specification refers to the situation where two transmissionsoverlap in time, as in this scenario an ATC would either not hear theSCT or the audio would be filtered out by the radio.

A typical speech DSB-AM signal can be fully described by the complextime-domain signal:

x(t)=A(1+kv(t))e ^((ω) ^(c) ^(t+θ)j)    Equation 1

where

t is the time in seconds

A is a gain constant (proportional to the transmitter Root Mean Square(RMS) power)

v(t) is the real-valued audio signal, normalised to (−1,+1) peak to peak

k is the modulation depth in the range (0,1) expressed as a percentage.

ω_(c) is the carrier frequency in radians/sec, typically approximately(2π)118 MHz.

θ is some notional phase offset (in radians) with respect to t=0

j is √{square root over ( )}−1

The spectrum (i.e. Fourier transform) of such a signal is shown in FIG.2—X(ω). The signal is centred on a theoretically infinitesimal carrierfrequency ω_(c). In reality, this carrier band is broadened by systemand transmission imperfections. There are ‘conjugate symmetric’sidebands either side of ω_(c), such that, for within the bandwidth ofv(t), X(ω_(c)+ω) is the same as X(ω_(c)−ω); equal magnitude andconjugate phase.

For convenient manipulation later, we express DSB-AM conjugate symmetryby first computing the conjugate of the carrier phasor as

$\begin{matrix}{c = \frac{{X\left( \omega_{c} \right)}^{*}}{{X\left( \omega_{c} \right)}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

where * indicates conjugation.

The conjugate symmetry property means that the following equality holds(approximate in practice, due to system imperfections and externaleffects).

(X(ω_(c)+ω)c)

(X(ω_(c)−ω)c)*    Equation 3

The imperfections in the system are due to noise, cancellationimperfections and superimposed signals (such as a weak secondarytransmitter due to SCT). In order to find these, the followingcalculation is performed:

Y(ω)=(X(ω_(c)+ω)(c)−(X(ω_(c)−ω)c)*    Equation 4

In order to perform such a calculation, properties of the primarycarrier signal (i.e. ω_(c) and c) must be first known. Once the primarycarrier has been identified, it can be isolated and removed, allowingsubsequent analysis of Y(ω) to determine whether an SCT has occurred.

FIG. 3 illustrates a high-level dataflow of an exemplary method(referred to as ‘Frequency Domain (FD) SCT detection’) for detecting thepresence of a secondary call transmission in an input signal. The inputis a high sample rate IQ (in-phase/quadrature) baseband time-series(real or complex) and the outputs are SCT detection results (forexample, as a tone inserted into the audio signal or a flag placed intoa data stream). Each step is described in more detail below thefollowing brief overview.

As used herein, the term “sum-signal” (and similar) preferably connotesa signal received by a receiver (for example an air traffic controlsystem). Such a sum signal preferably comprises a primary carriersignal, noise, and potentially a secondary carrier signal (wherepresent); the term “sum” merely implies, preferably, that such elements(primary carrier signal, noise, etc) are present in one and the samesignal.

A sum signal is received and converted to an IQ baseband sample. Thissignal is decimated 300 (downsampled) removing unnecessary frequencycomponents so as to reduce the load on later processing steps.

The decimated signal is sampled using an overlapping, sliding windowbuffer 302 which stores a given length of signal to be processed.Sampling the signal means that the entire signal does not need to beprocessed in one go, improving the latency of detection and reducingprocessor load.

The length of the buffer is determined by the trade-off betweenprocessor load in analysing lengthy samples and the increased detectionaccuracy (i.e. high signal-to-noise ratio) longer samples afford. Thesampling rate (i.e. number of windows per second) is determined by atrade-off between processor load in processing large numbers of windowswithin a short time-period and latency of SCT detection.

Each window sample is then input into a Fast Fourier Transform (FFT)304—outputting X(ω)—for further processing in the frequency domain. AnFFT is preferable to a continuous Fourier Transform (FT) as it is muchless processor-intensive. Other discrete transforms such as wavelettransforms or spectral line filters may be used.

The decimation step may introduce ‘decimator ripple’ in the frequencydomain output, this is corrected for at step 306 before any furtherprocessing.

The frequency of the primary carrier transmission is estimated 308, andthe FFT output is down-converted 310 based on this frequency. Thein-phase elements to the primary carrier transmission are then cancelledby subtracting the conjugate of the negative sideband frequencies of theprimary signal from their counterpart positive sideband frequencies inthe (decimated, down-sampled, frequency domain) sum signal 312.

The remaining signal—Y(ω)—is due to phase noise or other signals atdifferent frequencies (which may be SCTs) to the main carriertransmission in the signal. This signal is analysed for peaks 316(defined by a threshold) above an estimated noise floor 314. These peaksare indicative of an SCT being present as they represent significantmagnitude parts of the signal which are not on the same carrierfrequency as the primary transmission (e.g. peaks corresponding to aheterodyne tone). However, other effects, such as mains hum and phasenoise may show up as peaks above a nominal noise floor. Noise effectssuch as these affecting the sidebands of the primary carrier aretypically symmetric about the primary carrier frequency, thus anasymmetry analysis 318 is performed to determine whether a particularpeak has a corresponding ‘mirror image’ peak. This analysis is performedusing an ‘asymmetry threshold’. The peak is also analysed for itsmagnitude (above the noise floor) as higher power peaks are more likelyto be secondary transmissions rather than variations in noise. These twoparameters (and/or others) are combined in a ‘Feature SpaceClassification’ 320 and an SCT can be signalled if a sample contains apeak exceeding the predetermined threshold(s).

This process is performed continuously for every sampled window of theincoming signal. It should be noted that the method has been shown assplit into numerous discrete steps whereas in practice many of thesesteps may occur simultaneously or as part of a single step.

The process described above (after sampling) is undertaken entirely onthe spectrum of time windows of signal rather than any time-series. Thisis significant as the main (distinguishable) physical difference betweenprimary and secondary transmissions is the slight difference in centralfrequency. Analysing the spectrum is thus addressing the fundamentalproblem. Furthermore, all of the above processes are mathematicallylinear, thus greatly reducing the potential of spurious artefacts beingintroduced, or for errors to propagate and become amplified as theprocess continues.

FIG. 4 shows a schematic diagram of a radio receiver 104 adapted toperform the processes involved in the detection of a secondary calltransmission as described above.

A signal is received by an aerial and is input to an Analogue-to-DigitalConverter (ADC) 402. The dotted section 400 represents a simplifieddigital radio receiver without any SCT detection capability. The digitalsignal is demodulated by demodulating unit 403, with assistance from acentral processor 422 and memory 424. This is then passed to an audiooutput unit 420 and audio is outputted. An actual digital radio mayinclude many additional components (such as tuning, filtering andamplifying circuitry), but such components are omitted for clarity inthis figure.

This audio extraction process occurs independently of the SCT detection,as this represents the primary purpose of the radio 104, to convertreceived signals into audio (or other useful information). Thecomponents used for SCT detection are shown outside of the dottedsection 400.

The digital signal is decimated (downsampled) by decimator 404 beforebeing sampled in a sliding window buffer 406. Each window is then passedthrough a Fast Fourier Transform (FFT) 408.

The spectrum outputted from the FFT has filters/windows 410 applied toit so as to produce the signal defined by Y(ω) in equation 4. Thisoutput is passed to a comparator 412, which, with logic circuitry 412and thresholds stored in memory 424, determines whether an SCT hasoccurred. If so, the operator is notified, for example by a tone beinginserted into the audio output and/or a flag (such as an indicator on auser interface) is raised via tone/flag generator 418. Other informationregarding the SCT, such as indication of a confidence level, ortimestamp of the event, may also be outputted.

FIG. 4 shows components separated for clarity whereas in reality many ofthese components may be combined as a single component (such as thecomparator, logic combined with the processor) or further split intoseparate components.

The following description further details the various steps brieflydescribed above.

Decimation 300

In a DSB-AM radio receiver, the intermediate digital signal afteranalogue to digital conversion is often at a higher sample rate than isrequired to support the DSB-AM sidebands of a primary signal.

The decimation stage 300 represents the context-dependent low-passfiltering and down-sampling that may be required to reduce the signalbandwidth to a value of e.g. ±7 kHz at a sample rate of f_(s)=14 kHz.For instance, such a bandwidth will support a primary DSB-AM signal with4 kHz audio bandwidth (A) and up to ±3 kHz of frequency error (B). Therelationship between A, B and f_(s) are illustrated below, withadditional example values:

Audio bandwidth on Maximum Primary Complex Sample Rate Primary DSBsignal Frequency Error after decimation (f_(s)) (kHz) (kHz) (kHz) A ±Bf_(s) = 2*(A + B) 5 4 18 3 3 12 4 3 14

The purpose of decimation is twofold: (1) to reduce the computationalload and (2) reject signals outside the band of interest for SCTdetection. The decimation step (and the subsequent ripple equalisation)would not be necessary if these issues are not of any relevance (e.g. ifthe analogue-to-digital converter has a low sample rate).

The decimator design preferably has a narrow transition region (forexample 10% of passband) with low passband ripple (0-3 dB) and highstopband attenuation (for example more than 40 dB) i.e. a typicalspecification for a high-quality decimator for audio applications. Atypical low-pass mask specification given the third set of parameters inthe above table would be ±1 dB of passband ripple up to 5 kHz, atransition region from 5 kHz to 7 kHz, and −60 dB of gain in thedecimation stopband.

Note that if the time-series is real-only, then a complex oscillator andmixer are required to down-convert the signal before the decimator. Thedecimation low-pass filter then requires sufficient stopband attenuationto adequately remove the frequency-shifted conjugate image.

Sliding window buffer 302

This stage presents the most recent T seconds block of sample data Mtimes a second to the subsequent processing stages as illustrated inFIG. 5. Blocks preferably have a high degree of overlap to maximise thechance of detecting a secondary transmission as soon as it starts.Typical values for this stage (for the ATC example discussed above) areT=2 seconds, M=4 Hz, in this case the longest time possible between anSCT event beginning and the end of one window—t_(max) is 1/M=0.25seconds. However, not all SCT events may be detected in such a shorttime period as the signal may be too weak; in such circumstances, due tothe overlap of windows, the next window would have 0.5 seconds of SCT todetect and so on. Thus a detectable constant SCT would be detectedwithin T+t_(max) (=T+1/M) seconds. In order to ensure overlap thefollowing identity must hold: T*M>1, but ideally at around 8 windowsoverlap, so T*M≧8.

The purpose is to allow strong signals to be detected quickly by thesystem at a coarse granularity in time, but also allow an adequatetime-history to allow the coherent integration and detection of weaksecondary signals.

In use, M times a second, a buffer comprising the last T seconds of datais processed. This results in each data block of length 1/M secondsbeing processed T*M times in total. For illustration T can be in therange 1 to 4 seconds and M can be in the range 2 to 16. T governs thecoherent integration period for detecting weak SCT signals and it is ofadvantage to be long and about the same length as typical primarytransmission utterances. The value of (1/M) governs the maximum latencyfor detecting strong SCT signals and it is advantageous for M to be highfor low latency. The processing load is proportional to the product T*M,thus there is a trade-off between performance and processor load whenselecting values of T and M.

Although in use a large number of window buffers will be processed, forclarity, the following description will solely focus on the processingof a single window.

Oversampled, Zero-Padded FFT 304

FIG. 6 illustrates how the current analysis window from the buffer ismapped into the FFT input with ‘zero padding’. The mapping isunconventional in that the buffer is split into two halves and the firsthalf is mapped into the final part of the FFT input and the second halfis mapped into the start of the FFT input, with zero-value inputsoccupying the intervening samples. This improves the operation offrequency domain down-conversion as described below.

The FFT size N_(FFT) is chosen to be around twice the size of the bufferwindow to provide sufficient oversampling for subsequent processing. Thechoice of oversampling ratio at approximately ×2 is a compromise betweentwo conflicting factors: (1) critical sampling at around ×1 oversamplingis not viable because down-conversion requires an unfeasibly longresampling filter for the required DSB-AM cancellation fidelity, (2) thesystem performance at say, >×3 oversampling yields negligibleperformance benefit at the expense of increased computational complexityin the FFT. Of course, oversampling ratios of greater than ×3 may beused if computational complexity is not an issue—for example if thefidelity of the cancelation is paramount.

For example with a signal sampling rate, f_(s), of 14 kHz and T=2seconds, the buffer is 28,000 samples long. This indicates that an FFTsize of N_(FFT)=65,536 (the oversampling ratio being 2.34) isappropriate; presuming that a standard Digital Signal Processing (DSP)library function is used requiring a power-of-two size (i.e.N_(FFT)=2^(n), where n

⁺, in the example above, n=16). The relationship between these variablesand example combinations are indicated in the table below:

Buffer Radix-2 FFT Sample Rate Blocksize Size Oversampling (kHz) T(seconds) (kSamples) (kSamples) Ratio f_(s) T C = f_(s)*T N_(FFT)N_(FFT)/C 10 2 20  64 (≈2¹⁶) 3.2 12 4 48  64 (≈2¹⁶) 1.3 14 6 84 128(≈2¹⁷) 1.5 16 8 96 128 (≈2¹⁷) 1.3

Depending on operational requirements/constraints, a larger or smalleroversampling ratio may be used. The larger the oversampling, the moreprocessor-intensive the resulting analysis would be (due to the greaternumber of discrete frequency ‘bins’ in the frequency domain) but thesystem would be more accurate due to (at least) the spectrum havinggreater resolution.

For later convenience, the FFT output vector is denoted as the vector xwith elements x_(i) where i={0,1 . . . , N_(FFT)−1} counting up from thezero frequency bin.

Decimator Ripple Equalisation 306

The low-pass filter discussed above with reference to decimation mayhave significant passband ripple in order to be implementable withrealistic cost. Passband ripple is an artefact manifesting in thespectrum of a transformed signal having had imperfect (i.e. non-square)band-pass filters applied to it.

The gain fluctuation across the band of interest can degrade the abilityto perform primary carrier double side-band cancellation as it affectsthe conjugate symmetry property exploited in equation 3. A low-cost andsimple way to compensate this effect is to calculate the ripple acrossthe decimated band H(ω) from the FFT of the impulse response caused bythe decimation, and apply gain and phase compensation to the output ofthe FFT of 1/H(ω).

The inverse transform 1/H(ω) is stored as a vector of N_(FFT) complexweights which is applied to the output directly after the FFT has beencomputed.

Although H(ω) is symmetric about zero hertz, it is not symmetric aboutthe primary carrier, so would not be cancelled out when calculatingY(ω)—which is described in more detail below.

Primary Carrier Frequency Estimation 308

The highest magnitude FFT output bin (denoted as bin j) is detected andits power and frequency are measured. This is asserted to be the primarycarrier (i.e. strongest sinusoidal tone) and these measurements arepassed on to the classification stage discussed in order to detect ifany primary signal is present. Identifying the primary carrier frequencyleads to identification of non-primary carrier signals (such as an SCT).

Taking the magnitude samples of the three FFT output bins {j−1, j, j+1}a parabolic (quadratic) curve may be fitted to the points, for exampleusing closed-form linear algebra. The fractional bin frequency f in therange of −0.5 to 0.5 of the maximum value of the fitted parabola istaken to be the best estimate of the true primary carrier frequencyω_(c). The oversampling of the FFT (e.g. twice oversampling) provides aninterpolated mainlobe of the primary carrier and thus facilitates anaccurate peak position estimate. Accurate primary carrier peakestimation allows for a more accurate down-conversion, leading toimproved subsequent DSB-AM cancellation as the centre point of thereflection is more accurate.

At this stage the width of the primary mainlobe may be assessed bysearching out from the peak in both negative and positive frequencyuntil bins that are <3 dB (approximately <0.5 in power) of the peak areidentified (i.e. full-width, half maximum (FWHM) of the primarymainlobe). Leading and trailing edges of the primary transmitter in theanalysis window cause wide mainlobes, and this measurement may be usefulin the later ‘feature classification’ stage for assessing thetime-domain activity of a primary transmitter.

Frequency-Domain Down-conversion 310

Frequency-domain down-conversion 310 is performed by generating afinite-impulse filter which shifts the frequency bins by −(j+f) bins(i.e. by ω_(c)) so that the underlying maximum of the primary carriermainlobe is shifted exactly on to the zero frequency bin. This stepeffectively makes the primary carrier signal symmetric about zero hertz,making later computation and determination of SCT events simpler.

The formula for the filter is given in Equation 5 where

N _(coeffs)=4, w=[0.3635819, −0.4891775, 0.1365995, −0.0106411]

w generates a Blackman-Nuttall window which has good sidelobeperformance. Other windows may be used such as ‘Kaiser’ or ‘Equiripple’windows, but cosine-family windows such as Hamming, Hann, Blackmanfamily have the implementation benefit of combining good sidelobeperformance with the precise and simple computation using cosines.

The value X_(LIM) sets the limits for the window (i.e. it is zero-valuedfor |x|>x_(LIM)), and hence defines the quality of the resampling (atypical value would be x_(LIM)=5). A small value is desirable in orderto minimise the processing complexity of down-conversion. The choice of_(xLIM) is discussed in more detail below with reference to FIGS. 7 and8.

$\begin{matrix}{{g(x)} = \left\{ \begin{matrix}{{\frac{\sin \; \pi \; x}{\pi \; x}{\sum\limits_{i = 1}^{N_{coeffs}}{w_{i}{\cos \left( {i\; {\pi \left( {1 + \frac{x}{x_{{LI}\; M}}} \right)}} \right)}}}};{{x} \leq x_{{LI}\; M}}} \\{0;{{x} > x_{{LI}\; M}}}\end{matrix} \right.} & {{Equation}\mspace{14mu} 5}\end{matrix}$

The components of this frequency domain down-conversion filter are shownin FIG. 7. This figure also shows the ‘half bin samples’ which may bepresent due to the FFT oversampling described above with reference toFIG. 6. The effect of these fractional bins are described in more detailbelow with reference to FIG. 8.

$\begin{matrix}{x_{i}:={\prod\limits_{k = {- x_{{LI}\; M}}}^{+ x_{{LI}\; M}}{{g\left( {k - f} \right)}x_{{({i + j + k})}{modN}_{FFT}}}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

Down-conversion is performed using Equation 6 as a circular convolutionon the FFT output x but only including the non-zero terms from Equation5 to minimise computational cost. For example, with x_(LIM)=5, only2x_(LIM)+1=11 (−5 to +5) multiply/accumulates are needed per bin. Thisis analogous to implementing a short Finite Impulse Response (FIR)filter.

Frequency domain convolution of two signals is analogous tomultiplication of their time-domain equivalents. In this case, theinverse Fourier transform of the g(x) term in Equation 6 is an arbitraryfrequency sinusoid with a sampling-dependent envelope function: this isunity when samples are taken on a grid at integer values of x (i.e. f=0)and (worst-case) has ramping and a zero point when samples are taken ona grid at halfway between FFT bins (i.e. f=±0.5) as illustrated in FIG.8. Other values of f create envelopes intermediate between theseextremes. Although this process would not be necessary if only integervalues of f were used, doing so would introduce errors into the centralfrequency and thus mean that the later asymmetry analysis would carrythrough these errors.

The mathematical explanation for the envelope phenomenon shown in FIG. 8is as follows. Equation 5 comprises the product of two terms; (1) asin(x)/x function with infinite support on x (which has too many termsto compute practically) and (2) a compactly supported window function(which makes g(x) economic to compute). In time domain, by analogy, thisis the circular convolution of (1) an arbitrary frequency sinusoid and(2) a band-pass filter corresponding to the frequency shifted IFFT ofthe window function. The output of this filtering process is unitamplitude sinusoid except where a phase discontinuity passes through thefilter where the two ends of the sinusoid are circularly “spliced”together. This creates the characteristic “dip” in the sinusoid envelopeillustrated in FIG. 8 which is worst-case when a 180 degree continuitypasses through (as occurs with the half-bin case).

FIG. 8 also explains the utility of the unconventional zero-paddingdescribed above of mapping the “1^(st) half” and “2^(nd) half” of theinput buffer to time-domain intervals where the envelope function isalmost exactly unity. The mapping of the second half of the time windowto the first part of the FFT input and vice versa means that the FFTinput maintains its time-order as the end of the first half iseffectively contiguous with the start of the second half (as the FFT canbe visualised as wrapped around the surface of a cylinder). Hence if theequivalent time-domain product is taken (by taking notional IFFTs of thefrequency domain convolution), we have the desired effect of the signalmultiplied by a unit-amplitude complex sinusoid in order effecthigh-quality, precise down-conversion of the primary signal. Slightdeviation from unity over the non-zero-padded part of the envelopefunction is permitted as a perfect standard rectangular window is notnecessary. A tolerance of deviation from the maximum of the envelopefunction of approximately 1% is preferable.

The choice of x_(LIM) is a function of the oversampling ratio

$\left( \frac{n_{FFT}}{f_{s} \times T} \right)$

so as to be the smallest value to minimise the computational complexityof the window filter whilst not impinging on the ‘flatness’ of theenvelope function. If x_(LIM) is too small, the envelope function wouldbegin to curve over the sections of the IFFT which contain the signaldata, resulting in the signal being modified prior to DSB-AMcancellation. The value of x_(LIM) which satisfies this trade-off hasbeen empirically found to be approximately (12/oversampling ratio).

The final stage in down-conversion is to rotate the FFT output such thatthe primary carrier is zero-phase (phase-rotation). This is performed byEquation 7 where x is the down-converted FFT output derived fromEquation 6.

$\begin{matrix}{x:={x\frac{x_{0}^{*}}{x_{0}}}} & {{Equation}\mspace{14mu} 7}\end{matrix}$

DSB-AM Cancellation (of Primary Signal) 312

DSB-AM cancellation 312 as discussed above is effected by applyingEquation 8 in order to generate an output vector y comprisingN_(FFT)/2+1 bins (the zero frequency bin and the right hand side of thespectrum). As Y(ω) is by mathematical definition conjugate symmetricabout zero for an ideal primary carrier, only computation of the righthand side (i.e. positive frequency) is necessary. Only magnitudeinformation is taken into y for the purpose of peak detection, hence themodulus is taken.

$\begin{matrix}{{y_{i} = {{x_{i} - \left( x_{{({N_{FFT} - i})}{mod}\; N_{FFT}} \right)^{*}}}};{i \in \left( {0,1,{\ldots \mspace{14mu} \frac{N_{FFT}}{2}}} \right)}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

The quality of DSB-AM cancellation 312 is dependent on the temporalcoherence of the primary signal. Phase noise on the primary carrier canlead to some feed through of tonal components in the sidebands which mayappear as distinct tones in Y(ω). A simple technique for identifyingsuch tones using the concept of power ‘asymmetry’ is described below.

Subtracting the conjugate of the negative frequencies from the positivefrequencies of the sum signal (after down-conversion) effectivelycancels out the part of the signal in-phase with the primary carrier(attenuating the frequency domain primary carrier within thesum-signal), leaving just signals which have introduced phase noise intothe sum-signal. These signals include phase noise (which would generallybe at a low-level across a wide range of frequencies) and specifictones, which would manifest as peaks in the frequency plot.

Noise Floor Estimation 314

SCT tones in y are characterised by isolated narrowband peaks against anoise floor after DSB-AM cancellation of the primary carriertransmission. Hence, in order to detect peaks, a noise floor estimatewhich is not biased by tonal peaks should be estimated. Noise levels maynot be constant over the whole frequency range in question, so the noiselevel at every frequency bin is estimated in order to 1) capturesecondary transmissions above the local noise level, but potentiallybelow the noise level elsewhere, and 2) discount frequency bins withhigher levels of noise than elsewhere. A single estimate of the noiselevel across the entire frequency spectrum would not be able to accountfor such circumstances, resulting in, in the case of 1) false negatives,and in the case of 2) false positives. Either of these scenarios isundesirable, false negatives particularly so in an ATC implementation assuch events could result in a dangerous situation.

An effective way to determine a frequency-dependent noise floorestimation is to calculate a moving-average of the magnitude across arange of bins centred around a particular frequency bin. If a largeenough bin range is used and peaks are not frequent, this would be anaccurate representation of the noise floor at that frequency bin. In oneexample a short sliding-window rank-order statistic filter is appliedwhich extracts the e.g. the median, power bin as the noise floorestimate. Analogous filters are used for removing impulsive noise fromotherwise smooth functions in applications like image processing.

This concept is expressed simply in Equation 9 where the median windowestimate is over ±N_(NFE) bins (a typical value is N_(NFE)=256 whenN_(FFT)=65536). If the window is too long, frequency-dependent changesin the noise floor are smoothed-out and the noise floor does not respondto local effects such as colouration from filters. On the other hand ifN_(NFE) is too short, legitimate SCT peaks may adversely bias the noisefloor estimate leading to them being smoothed and subsequentlydiscounted. A value for N_(NFE) of approximately √{square root over(N_(FFT))} has been found to satisfy this trade-off, but otherinformation (such as known noise sources) may be taken into account inthe choice of N_(NFE).

An issue occurs when applying the window to the very start and end of ywhere non-existent bins are addressed outside the boundary. A solutionis to reflect-in the missing bins from the respective boundary such thate.g. bin i=−1 comes from bin i=+1, and similarly so, for the end of y.

$\begin{matrix}{{n_{i} = {{median}\left( y_{i - {N_{NFE}\ldots \; i} + N_{NFE}} \right)}};{i \in {\left( {0,1,{\ldots \mspace{14mu} \frac{N_{FFT}}{2}}} \right){FFT}}}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

Median filtering is costly to compute in terms of procession time andpower. A practical optimisation is to decimate y by summing contiguousblocks of D₁ samples and then using a much shorter median filter over±D₂on the resulting decimated signal. The aggregate window size isN_(NFE)=D₁ D₂ For instance, D₁=16 and D₂=16 when N_(NFE)=256. This haslittle performance loss when the time series y is dominated by the noisefloor and has sparsely located peaks. In one embodiment D₁=D₂=√{squareroot over (N_(NFE))}, this splits the processing load evenly between thelinear moving average process and the non-linear median filteringprocess. In other embodiments fewer, larger windows may be taken oralternatively, more, smaller windows. The choice of length of windowsD₁, D₂ is also dependent on the trade-off between too short beingdominated by peaks and too long missing the trend of the noise, forexample D₁ and D₂ could each vary between 4 and 64 as a generalillustration in these circumstances.

The median is the default rank-order statistic to draw out, but othermeasures of central tendency are possible, for example the 40^(th)centile, which will be less biased by peaks, but more susceptible to lowpower noise samples.

Peak Detection of Secondary Carriers 316

Peaks are identified in y by identifying local maxima, wherey_(i)>y_(i+1) and y_(i)>y_(i+1). Performing just this analysis may pickup a lot of spurious fluctuations in the noise floor, for this reasononly peaks (i.e. values of y_(i)) that satisfy a certain predefinedthreshold (peak_metric_thresh) are identified as SCT candidates. Examplevalues for peak_metric_thresh are provided below with reference to FIGS.11 to 14, but may vary from around 0.85 to 3 (or greater than 3)depending on the situation.

In one embodiment this is where the distinct peaks in y are 10^(peak)^(_) ^(metric) ^(_) ^(thresh) times higher than the (local) noise floorn. This is denoted the subset P of the set of all possible i values (binindices) which satisfies Equation 10.

$\begin{matrix}{{\left( {y_{i} > {10^{{peak}\; \_ \; {metric}\; \_ \; {thresh}}n_{i}}} \right)\mspace{14mu} {AND}\mspace{14mu} \left( {y_{i} > y_{i - 1}} \right)\mspace{14mu} {{AND}\left( {y_{i} > y_{i + 1}} \right)}};\left( {1,{{2\mspace{14mu} \ldots \mspace{14mu} \frac{N_{FFT}}{2}} - 1}} \right)} & {{Equation}\mspace{14mu} 10}\end{matrix}$

This gives rise to the value of peak metric (principally for diagnosticpurposes) in Equation 11.

$\begin{matrix}{{{p(i)} = {\log_{10}\frac{y_{i}}{n_{i}}}};{i \in P}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

The threshold peak_metric_thresh is preferably a system-set parameterwhich may be calculated once upon calibration of the system;alternatively it may be dynamically calculated so as to result in asystem with a specific false-positive rate. This may be useful if thevariance in the noise floor (i.e. the accuracy of the noise floorestimate) changes over time so that the system becomes more prone tofalse negatives (if the variance decreases) or it becomes more prone tofalse-positives (the variance increases). In an average situation, avalue for the peak metric threshold p(i) would be between 1 and 4, morepreferably between 2 and 3 as a general illustration in thesecircumstances.

Another metric that may be used to reduce the number of candidate peaksis to specify that two peaks must be separated by a minimum frequencyotherwise they are treated as a single peak (i.e. the smaller peak isdisregarded). The threshold min_freq_sep is defined. In one example thisis between 5 Hz and 50 Hz, preferably between 7 Hz and 15 Hz, andpreferably approximately 10 Hz. Disregarding the smaller peak of aclosely separated pair of peaks has negligible impact on the capabilityto detect genuine secondary tones when peak detections are sparselyseparated. Such a feature allows strong peaks from e.g. 400 Hz mains hum(which are highly conjugate-symmetric) to absorb their own sidelobefeatures which are much weaker in power but more asymmetric and thus cancause false positives. The method identifies the weaker peaks from theset P which are within +/−min_freq_sep of the current secondary tonecandidate being analysed, and marks them for deletion from set P byplacing them in the set Q as follows (with commentary accompanying eachstep):

Q={ }create an empty set Q

for all i; i∈P i is a counter for all candidate peaks in the set P

for all j; j∈P j is a counter for all candidate peaks in the set P

if (|x_(j)|<|x_(i)|) AND

$\left( {\frac{{{i - j}}f_{s}}{N_{FFT}} < {\min {\_ freq}{\_ sep}}} \right)$

every peak j is compared with every other peak i in the set P for if jhas a lower magnitude than i and is within the minimum frequencyseparation from i (i and j are frequency bin numbers so are firstconverted to a real frequency difference by multiplying by the samplingf_(s) and dividing by the total number of bins N_(FFT)). It should benoted that when j==i the condition is not met due to the strictmagnitude inequality.

Q:=Q ∪j the peaks j that satisfy the above are added to the set Q

end (if)

end (for)

end (for)

Power Asymmetry Analysis 318

Given secondary tone candidate indices in P, a non-negative real-valuedasymmetry metric is computed using Equation 12. This is a measure of howasymmetric the power is between positive and negative frequencies (withrespect to the down-converted primary carrier at zero frequency).

$\begin{matrix}{{{a(i)} = {{\log_{10}\frac{x_{i}}{{N_{FFT} - i}}}}};{i \in P}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

An asymmetry analysis favours ‘legitimate’ SCT events over other phasenoise as SCT events have (by definition) a central frequency offset fromthat of the primary carrier and are thus asymmetric about primarycarrier (and, after down-conversion, are asymmetric about zero hertz).There is a low probability of another tone precisely at the oppositefrequency sign as this would correspond to a third SCT at a veryspecific frequency.

In contrast, “worst-case” primary signals with the deleteriousproperties of (1) high phase noise and (2) voice sidebands contaminatedwith interference tones (from e.g. mains electricity) generate secondarycarrier candidates which are very symmetric in power (from the coredefinition of DSB-AM conjugate symmetry).

Hence the asymmetry metric a(i) provides a useful way to exploit valuesthat are pre-computed elsewhere in the process (i.e. bins from thedown-converted X(ω) in vector x) to reject false positives from poorquality primary transmitters.

A threshold, asym_metric_thresh, for the value of a(i) is defined wherepeaks not meeting this threshold are discarded as being too symmetrical,and thus unlikely to be SCTs. The asymmetry threshold provides a meansto discount peaks which have a high residual power following subtractiondue to the fact that the symmetric peaks had a high power prior tosubtraction—for example if the signal has a high level of noise (whichis not perfectly symmetrical), or due to external effects such as mainshum. FIGS. 12, 13(b) and 13(c) below show scenarios where the asymmetrythreshold is utilised to reduce the false-positive rate by limiting thenumber of events above the power threshold which would otherwise bedeemed to be SCT events.

Feature Space Classification 320

Before a candidate peak from set P can be determined as an SCT event, anumber of checks may be performed.

In order for an SCT to be present, there must be first the presence of aprimary peak. This eliminates false positives when there is notransmission being received. A threshold primary_pk_thresh is definedwhere SCT analysis is only undertaken if the primary peak is above thisthreshold. This threshold is corrected by the amount of gain applied tothe signal (AGC_gain) so as to measure the absolute power of the primarysignal.

A threshold is also set for the maximum allowed width of the primarypeak, primary_bw_thresh, where SCT analysis is only undertaken if thewidth of the primary carrier peak is greater than this threshold. Thisensures that a certain lower bound is met on the mark-space ratio of theprimary transmitter in the analysis window, for example it may bedesirable for the primary transmission to occupy at least 50% of thetime window. This can prevent some anomalies due to rising edgesentering or trailing edges leaving the analysis window. The width of theprimary carrier peak is an output which is simple to generate and whichprovides some clear information about the temporal activity of theprimary transmitter.

The following section describes logic which may implement theclassification part of the method.

Inputs from Primary Carrier Frequency Estimation

The following additional inputs are used for detecting the presence of aprimary signal (and have associated thresholds):

primary_pk

Magnitude value of primary peak

primary_bw

Primary peak 3 dB width in bins (FWHM)

AGC_gain

The Automatic Gain Control magnitude gain applied elsewhere in thereceiver.

Impact of AGC in the RX chain

Automatic Gain Control (AGC) will modulate the dynamic range of signals;therefore the primary_pk value is scaled by the amount of applied AGCand thus needs to be re-scaled by the reciprocal of the AGC gain inorder to have an absolute power in terms of dBm.

Example Decision Logic

The following decision logic is given as an example of how to generate aBoolean detection output.

if (primary_pk>(primary_pk_thresh/AGC_gain)) AND

(primary_pk>primary_bw_thresh) AND

there exists any a(i)>asym_metric_thresh; i∈P

then

SCT_detect=TRUE

else

SCT_detect=FALSE

end (if)

This analysis would give a Boolean ‘yes’ or ‘no’ to any peak that haspassed the previous filtering stages so that it remains in candidate setP (e.g. that it is above the peak threshold and is not close infrequency to another peak).

The exact values of the parameters used in the analysis (e.g. a(i) andp(i)) can be used in a ‘quadrant’ analysis, wherein the combination ofthem in a feature space leads to a positive SCT determination.

A more generalised analysis is to fit a suitable likelihood densityfunction of the form prob(peak_metric, asymmetry_metric) given SCTpresent (“H1”) or SCT absent (“H0”) and then computing a likelihoodratio to make the decision. The exact form of the likelihood functionwould depend on the application, as well as other factors such asdesired false positive rate.

A more sophisticated algorithm than the decision logic described above,with some statistical modelling of the parameter density functions underdifferent H1/H0 hypotheses (e.g. Gaussian Mixtures Model, FuzzyClustering, Neural Network, or Support Vector Machines) would be capableof generating a ‘soft’ output with a confidence score, for examplebetween zero and one.

Such a confidence level could be fed-back to the end user forinformation and/or calibration purposes.

Simulation Results

To illustrate the operation of the proposed method the following‘difficult’ signal scenario comprising the presence of SCT isdemonstrated, the scenario featuring:

Primary DSB-AM signal carrying voice audio and additive loud 400 Hzmains hum

Primary carrier frequency error

Significant phase noise on the primary carrier

Secondary DSB-AM signal carrying voice

Additive White Gaussian Noise (AWGN)

FIG. 9 shows the spectrum X(ω) of the input (a) and output (b) signalsof Frequency Domain Down-Conversion. The primary carrier, voicesidebands, 400 Hz mains tone sidebands and the secondary signal(creating an SCT-present scenario) are marked. After down-conversion,the primary carrier is shifted to zero-frequency making the two voiceand 400 Hz mains sidebands and the carrier of the single secondarysignal respectively symmetric and asymmetric about zero-frequency, asdiscussed above.

FIG. 10 illustrates the results of the DSB-AM cancellation spectrum Y(ω)(a) and the noise floor estimated spectrum N(ω) (b) in comparison to thesuperposed positive and negative frequency halves of X(ω). DSB-AMcancellation has achieved around 25 dB attenuation of the 400 Hz tonewith negligible attenuation of the secondary carrier. This is becausethe 400 Hz mains hum modulates the primary carrier and is thusconjugate-symmetric with respect to the primary carrier. This means thisfeature is largely attenuated by the proposed frequency domain DSB-AMcancellation stage. However the secondary carrier is not conjugatesymmetric with respect to the primary carrier and is not significantlyattenuated.

The noise floor estimate, N(ω)—shown in FIG. 10(b), follows theunderlying spectral envelope of Y(ω) without much bias from isolatedpeaks in Y(ω). Note that imperfect DSB-AM cancellation of the(semi-coherent, poor quality) primary signal has led to somefeed-through of primary voice spectrum which is followed by the noisefloor estimate N(ω).

FIG. 11 illustrates detected peaks (the peak_metric_thresh is set low toa value of 0.85 to allow false detections through for characterisation).Two peaks are correctly detected for respectively the 400 Hz mains toneand secondary carrier. Though the peak metrics are of comparablemagnitude (shown in FIG. 11(a)), the asymmetry metrics are different(FIG. 11(b)).

By extension, if a Monte Carlo run of 1000 simulations is performed withthe same parameters, but randomised noise and frequency offsets, weobtain the informative scatterplot in FIG. 12 of peak metric versusasymmetry metric. There are two distinct clusters caused by (1) highlypower-symmetric detections due to poorly-cancelled 400 Hz tones and (2)highly asymmetric tones due to genuine secondary carrier. Feature spacedesign as described above may be used to distinguish between these twodifferent sets of candidate peaks even with ‘difficult’ signalparameters.

Various thresholds may be used to determine legitimate SCT events. FIG.14 illustrates the utility of such thresholds. For illustration,empirically setting the asym_metric_thresh≈0.4 and thepeak_metric_thresh≈3.5 excludes most of the 400 Hz false positives andstill includes the majority of the genuine secondary signal cluster truepositives as shown by FIG. 12.

Three further scenarios are illustrated in FIG. 13, as described in thetable below:

Primary 400 Hz Mains SCT absent SCT present Absent FIG. 13(a) FIG. 13(b)There are a few isolated Most of the SCT true points, well below thepositives lie in the proposed thresholds. No top right quadrant de-false positives. scribed by the two proposed thresholds. Present FIG.13(c) FIG. 12 There is a cluster of points, As discussed above.exceeding the peak threshold, but not the asymmetry threshold. Thisshows the value of the proposed dual threshold idea. No false positiveswould be generated.

Such ‘feature space classifications’ may be provided to a user forsystem analysis, or the SCT determination may be performed directly onthe data with no graphical output.

‘Mixed domain’ SCT detection

An alternative embodiment where both the time series and the spectrum ofthe received signal are processed is described below. This embodimentmay be preferable if processing power is limited, as processing largeamounts of FFTs and their outputs can be processor intensive, especiallyif the FFT is significantly oversampled.

FIG. 14 shows a high-level flow diagram for the ‘mixed domain’ method;many of the steps having corresponding steps in the frequency domain SCTdetection method. The detail relating to the corresponding stepsdescribed above applies to this alternative embodiment unless explicitlyindicated otherwise.

The first steps are as described previously, wherein the incoming signalis decimated 300 and ‘chopped up’ into overlapping windows 302.

The method then branches, with one branch performing an FFT 500,estimating the frequency 502 and phase 504 of the primary transmissionin the signal. The phase may be estimated by determining the phase ofthe samples used in determining the peak (e.g. the highest magnitudesample and the two either side). The highest magnitude samples wouldmost likely be from the primary carrier so are most likely to have theprimary phase. The primary carrier frequency and phase are used todown-convert 505 the time-domain windows by mixing each window with acomplex sinusoid with the same frequency and phase-offset as the primarycarrier transmission.

The signal can be illustrated by FIG. 15 where the in-phase (I) andquadrature (Q) components of a frequency down-converted signal (x′(t))are plotted. If there were only perfect, phase noise free, primarycarrier transmission, this vector would lie at constant 0 with itsmagnitude (i.e. length) changing with time. If there are any additivesignals (such as SCTs or phase noise), the vector's angle would alsochange.

In order to measure this part of the signal, the signal is phase-rotatedby θ and the part of the vector moving along the Q axis is measured.This step corresponds to the ‘Quadrature split’ 506 step in FIG. 14.This process is mathematically linear and so information is preservedand no artificial intermodulation effects are propagated through to thefollowing processing steps.

A real-only input FFT 508 is performed on the Q component of thephase-rotated signal. This provides a spectrum from which peaks aredetected 510 corresponding to the out-of-phase components of theoriginal signal.

The analysis of these peaks so as to determine the presence of an SCTevent then follows in the same way as described above.

Alternatives and Modifications

The above specification refers primarily to the situation where twosimultaneous transmissions are present, but the same system would beable to alert the user to any number of simultaneous transmissions. Thespecification has been limited to the former scenario as this isstatistically far more likely.

Furthermore, the specification above is primarily concerned withsimultaneous voice transmissions received by an Air Traffic Controller,but it will be appreciated that the signal does not necessarily have tobe voice transmissions. For example, it may be digital informationencoded into an AM radio transmission.

In the above description, the conjugate of the negative frequencysideband is subtracted from the related positive frequency sideband ofthe sum-signal so as to cancel out the primary carrier. The oppositeoperation is equally possible whereby the conjugate of the positivefrequency sideband is subtracted from the related negative frequencysideband of the sum-signal.

Various ranges and/or values are provided in this description, oftenwith reference to specific embodiments, notably being derived fromvalues such as buffer window size T, sampling rate f_(s) andaudio/signal bandwidth. Those skilled in the art would understand thatfor different applications or operating conditions, the system andmethod may operate more effectively with these values modified.

It will be understood that the present invention has been describedabove purely by way of example, and modifications of detail can be madewithin the scope of the invention.

Reference numerals appearing in the claims are by way of illustrationonly and shall have no limiting effect on the scope of the claims.

What is claimed is:
 1. A method of determining the presence of asecondary carrier signal in a time-domain sum-signal including a primarycarrier signal, the method comprising: transforming the sum-signal intothe frequency domain; extracting at least one peak corresponding to aheterodyne tone from the transformed sum-signal; determining thepresence of a secondary carrier signal in the sum-signal based on saidat least one peak.
 2. A method according to claim 1 further comprisingidentifying a primary carrier signal within the sum-signal.
 3. A methodaccording to claim 1 or 2 further comprising determining a conjugate ofa sideband of the frequency-domain primary carrier signal; andattenuating the primary carrier signal by using said conjugate of thesideband of the primary signal.
 4. A method according to claim 3 whereinthe conjugate of the sideband of the primary signal is subtracted fromthe opposing frequency sideband of the sum-signal.
 5. A method accordingto any preceding claim wherein the step of transformation into thefrequency domain is performed using a Fourier Transform (FT).
 6. Amethod according to any preceding claim wherein the step oftransformation into the frequency domain is performed using a discretetransform comprising input and output bins.
 7. A method according toclaim 6 wherein the signal is split and mapped onto the input of saidtransform with a larger size than the signal, wherein in a central partof said transform comprises zero-valued input bins.
 8. A methodaccording to claim 7 wherein a second half of said signal is mapped ontoa first part of the transform input and a first half of the signal ismapped onto a final part of the transform input.
 9. A method accordingto any of claims 2 to 8 wherein identifying a primary carrier signalcomprises estimating a primary carrier frequency.
 10. A method accordingto claim 9 wherein estimating the frequency of a primary carriercomprises determining at least one of the highest magnitude frequencyoutput bin and determining the peak frequency.
 11. A method according toclaim 10 wherein the three highest frequency output bins are determinedand a quadratic curve is fitted so as to interpolate the peak frequency.12. A method according to claim 9 or 10 further comprisingdown-converting the frequency-domain sum signal based on said estimatedfrequency.
 13. A method according to claim 12 further comprisingphase-rotating the frequency-domain down-converted sum-signal.
 14. Amethod according to claim 12 or 13 wherein the down-conversion isperformed by convolving the transform output with a window filter.
 15. Amethod according to claim 14 wherein the window filter comprises aclosed-form cosine function.
 16. A method according to claim 15 whereinthe window filter comprises a Blackman family window, preferablyBlackman-Nuttall window.
 17. A method according to claim 14 wherein thewindow filter comprises one of Kaiser or Equiripple.
 18. A methodaccording to any preceding claim wherein determining the presence of asecondary transmission comprises performing a symmetry analysis on saidpeak.
 19. A method of determining the presence of a second carriersignal in a time-domain sum-signal, the method comprising: identifying aprimary carrier signal within the sum-signal; attenuating the primarycarrier signal from within the sum signal; extracting at least one peakcorresponding to a heterodyne tone; performing a symmetry analysis onsaid at least one peak to determine the presence of a secondarytransmission.
 20. A method according to claim 18 or 19 whereinidentifying a primary carrier signal comprises estimating a primarycarrier frequency.
 21. A method according to claim 19 or 20 whereinidentifying a primary carrier signal comprises estimating the phase ofthe primary carrier.
 22. A method according to claim 20 comprisingtransforming the sum-signal into the frequency domain.
 23. A methodaccording to claim 22 wherein estimating the frequency of a primarycarrier within the sum-signal comprises determining at least one of thehighest magnitude frequency output bin and determining the peakfrequency.
 24. A method according to claim 21 comprising transformingthe sum-signal into the frequency domain.
 25. A method according toclaim 24 wherein the step of transformation into the frequency domain isperformed using a discrete transform comprising input and output bins.26. A method according to claim 25 wherein the phase estimation isperformed by determining at least one highest magnitude frequency outputbin and determining the phase of the peak frequency component.
 27. Amethod according to claim 22 or 25 wherein the three highest frequencyoutput bins are determined and a curve is fitted so as to interpolatethe peak frequency.
 28. A method according to claim 27 wherein thefitted curve is a quadratic curve.
 29. A method according to any ofclaims 19 to 28 wherein following down-conversion, the quadraturecomponent of the time-domain sampled signal is transformed into thefrequency domain prior to peak extraction.
 30. A method according to anyof claims 19 to 29 wherein the down-converting comprises mixing thesampled signal with a sinusoid with a frequency and phase correspondingto an estimated frequency and phase of the primary carrier.
 31. A methodaccording to claim 22 or 24 wherein the transformation into thefrequency domain is a Fourier Transform (FT), preferably a Fast FourierTransform (FFT).
 32. A method according to any of claims 18 to 31wherein the symmetry analysis comprises: determining a measure of theratio of the magnitude of a peak at a certain frequency above a centralfrequency with the magnitude of the signal at the correspondingfrequency below the central frequency.
 33. A method according to claim32 comprising comparing said asymmetry ratio to a pre-determinedthreshold.
 34. A method according to claim 32 or 33 wherein themagnitude of the peak is used in conjunction with said ratio indetermining the presence of a secondary transmission.
 35. A methodaccording to claim 34 comprising producing a confidence score of asecondary carrier transmission being present based on the peak magnitudeand asymmetry ratio.
 36. A method according to any preceding claimwherein the presence of a secondary transmission is determined only if apeak corresponding to the carrier of a primary transmission is present.37. A method according to claim 36 wherein the presence of a secondarytransmission is determined only if the magnitude of said primary carrierpeak is above a pre-determined threshold.
 38. A method according toclaim 36 or 37 wherein the presence of a secondary transmission isdetermined only if the width of said primary carrier peak is below apre-determined frequency threshold.
 39. A method according to anypreceding claim wherein following peak extraction, if two peaks arewithin a minimum frequency separation of one another, the peaks arecombined into a single peak prior to determination of the presence of asecondary carrier.
 40. A method according to claim 39 wherein theminimum frequency separation is between 5 Hz and 50 Hz, preferablybetween 7 Hz and 15 Hz, preferably approximately 10 Hz.
 41. A methodaccording to claim 39 or 40 wherein the peak with the lower magnitude isdiscarded.
 42. A method according to any preceding claim wherein thesum-signal is decimated so as to reduce the bandwidth.
 43. A methodaccording to claim 42 wherein the frequency domain transform output isgain-transformed so as to compensate for decimator ripple.
 44. A methodaccording to claim 43 wherein the gain transformation is the reciprocalof the gain due to the magnitude spectrum of the decimator.
 45. A methodaccording to any preceding claim wherein the sum-signal is sampled. 46.A method according to any preceding claim wherein the sum-signal issampled in overlapping blocks.
 47. A method according to claim 46wherein the sampling consists of the most recent T seconds of the signaland the sampling rate is M times per second, where T*M>1.
 48. A methodaccording to claim 47 wherein T is between 1 and 4, and M is between 2and
 8. 49. A method according to claim 48 wherein T=2 and M=4.
 50. Amethod according to any preceding claim further comprising: estimating anoise floor of the down-converted signal; subtracting a measure of saidnoise floor from the signal prior to peak extraction.
 51. A methodaccording to claim 50 wherein the noise floor estimation comprisesperforming a moving-average.
 52. A method according to claim 51 whereinthe moving average comprises summing contiguous blocks of D₁ samples andcalculating the median across D₂ of said blocks.
 53. A method accordingto claim 52 wherein D₁ is approximately equal to D₂.
 54. A methodaccording to any preceding claim further comprising alerting an operatorto the presence of a secondary transmission.
 55. A method according toclaim 54 wherein alerting an operator comprises inserting a tone into anaudio output.
 56. A method according to claim 54 or 55 wherein alertingan operator comprises indicating the presence of a secondarytransmission on a user interface.
 57. A method according to any ofclaims 54 to 56 wherein alerting an operator comprises indicating theconfidence level of the presence of a secondary transmission.
 58. Amethod of reducing windowing artefacts in a time/frequency transform ofa signal: applying a windowing function to a signal; mapping the signalonto the input of an oversampled transform; wherein a central part ofthe transform input has zero-valued input bins; performing atime/frequency transform; outputting a frequency spectrum of the signal.59. A method according to claim 58 wherein the transform is a Fouriertransform
 60. A method according to claim 58 or 59 wherein a second halfof the signal is mapped onto a first part of the transform input and afirst half of the signal is mapped onto a final part of the transforminput.
 61. A method according to claim 58 or 60 further comprising thestep of determining the presence of a secondary carrier signal from thefrequency spectrum of the signal.
 62. A method according to claim 61further comprising alerting a user to the presence of a secondarycarrier signal.
 63. A method according to any preceding claim whereinthe signal comprises voice communication.
 64. A method according toclaim 63 wherein the voice communication is transmitted from an aircraftand intended to be received by an air traffic controller.
 65. Anapparatus adapted to carry out a method according to any precedingclaim.
 66. An apparatus for determining the presence of a secondarycarrier signal in a time-domain sum-signal including a primary carriersignal, the apparatus comprising: means for transforming the sum-signalinto the frequency domain; means for extracting at least one peakcorresponding to a heterodyne tone from the transformed sum-signal;means for determining the presence of a secondary carrier signal in thesum-signal based on said at least one peak.
 67. An apparatus fordetermining the presence of a second carrier signal in a time-domainsum-signal, the method comprising: means for identifying a primarycarrier signal within the sum-signal; means for attenuating the primarycarrier signal from within the sum signal; means for extracting at leastone peak corresponding to a heterodyne tone; means for performing asymmetry analysis on said at least one peak to determine the presence ofa secondary transmission.
 68. An apparatus for reducing windowingartefacts in a time/frequency transform of a signal: means for applyinga windowing function to a signal; means for mapping the signal onto theinput of an oversampled transform; wherein a central part of thetransform input has zero-valued input bins; means for performing atime/frequency transform; means for outputting a frequency spectrum ofthe signal.
 69. An apparatus according to any of claims 65 to 68comprising a radio.
 70. An apparatus according to claim 69 wherein theradio is a software-defined radio.
 71. A method substantially asdescribed herein and/or illustrated with reference to the accompanyingdrawings.
 72. An apparatus substantially as described herein and/orillustrated with reference to the accompanying drawings.
 73. A radiosubstantially as described herein and/or illustrated with reference tothe accompanying drawings.